Evaluation of Fano resonance and phase analysis of plasma induced transparency in photonic nanostructure based on equivalent circuit analysis

Fano resonance and plasma induced transparency (PIT) have been widely observed in various plasmonic nanostructures. Fano resonance takes place in weak coupling regime where coupling constant between two electromagnetic modes is lower than damping constant of system. Hence, extracting coupling and damping coefficients from resonance spectrum is the key to distinguish between Fano resonance and other resonances. In this paper, we propose a simple and realizable coupled LC circuit to analyze Fano resonance and PIT. Weak and strong coupling regime are distinguished by comparing coupling constant with damping constant. Meanwhile, we gain deep insight into Fano resonance and PIT in circuit by analyzing circuit phase and understand their connection with resonance in photonic structure. Furthermore, we extend the equivalent circuit model to the field involved short-range plasmon polarization or multi-orders dark modes. Since there are no specific parameters associated with photonic nanostructure, the proposed equivalent circuit can be used in most plasmonic resonance system as an universal model.

Compact, flexible and highly selective wideband complementary FSS with high angular stability

This article presents a novel miniaturized (0.105λ0 × 0.105λ0) flexible complementary frequency selective surfaces (CFSS) structure with sharp band edge selectivity and very high angular stability. To explore two diverse applications as a passband and stopband filter, a novel complementary convoluted square loop (CCSL) type structure has been designed and investigated on ultrathin dielectric material of thickness 0.0023λ0. The second-order wide controllable passband with fractional bandwidth of 19.23% (−3 dB) and remarkably wide stopband of 64.7% (−10 dB) and 54.8% (−20 dB) respectively have been achieved by using a cascaded resonating structure which is composed of asymmetrical meandered CCSL array, arranged on two ultrathin dielectric layers with air foam separation. This particular format would lead to sharp band edge selectivity with steep roll-off (72.43 dB/GHz) and an excellent passband selectivity factor (0.731). An equivalent lumped LC circuit in conjunction with the transmission line model has also been adopted to comprehend the physical mechanism of the proposed single layer and double layer structures. Further, better passband and stopband angular stability at an oblique incident angle of 45° and the bending characteristics have also been investigated thoroughly for the proposed flexible CFSS to check their employability in different conformal structures with WiMAX passband and WLAN stopband application.

Nonlocal fractal calculus based analyses of electrical circuits on fractal set

Purpose The purpose of this paper is to present the analyses of electrical circuits with arbitrary source terms defined on middle b cantor set by means of nonlocal fractal calculus and to evaluate the appropriateness of such unconventional calculus. Design/methodology/approach The nonlocal fractal integro-differential equations describing RL, RC, LC and RLC circuits with arbitrary source terms defined on middle b cantor set have been formulated and solved by means of fractal Laplace transformation. Numerical simulations based on the derived solutions have been performed where an LC circuit has been studied by means of Lagrangian and Hamiltonian formalisms. The nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been derived and the local fractal calculus-based ones have been revisited. Findings The author has found that the LC circuit defined on a middle b cantor set become a physically unsound system due to the unreasonable associated Hamiltonian unless the local fractal calculus has been applied instead. Originality/value For the first time, the nonlocal fractal calculus-based analyses of electrical circuits with arbitrary source terms have been performed where those circuits with order higher than 1 have also been analyzed. For the first time, the nonlocal fractal calculus-based Lagrangian and Hamiltonian equations have been proposed. The revised contradiction free local fractal calculus-based Lagrangian and Hamiltonian equations have been presented. A comparison of local and nonlocal fractal calculus in terms of Lagrangian and Hamiltonian formalisms have been made where a drawback of the nonlocal one has been pointed out.

A Low Excitation Working Frequency Capacitively Coupled Contactless Conductivity Detection (C4D) Sensor for Microfluidic Devices

In this work, a new capacitively coupled contactless conductivity detection (C4D) sensor for microfluidic devices is developed. By introducing an LC circuit, the working frequency of the new C4D sensor can be lowered by the adjustments of the inductor and the capacitance of the LC circuit. The limits of detection (LODs) of the new C4D sensor for conductivity/ion concentration measurement can be improved. Conductivity measurement experiments with KCl solutions were carried out in microfluidic devices (500 µm × 50 µm). The experimental results indicate that the developed C4D sensor can realize the conductivity measurement with low working frequency (less than 50 kHz). The LOD of the C4D sensor for conductivity measurement is estimated to be 2.2 µS/cm. Furthermore, to show the effectiveness of the new C4D sensor for the concentration measurement of other ions (solutions), SO42− and Li+ ion concentration measurement experiments were also carried out at a working frequency of 29.70 kHz. The experimental results show that at low concentrations, the input-output characteristics of the C4D sensor for SO42− and Li+ ion concentration measurement show good linearity with the LODs estimated to be 8.2 µM and 19.0 µM, respectively.

Development of an electromagnetic device for studying the electrophysical properties of agricultural products

The problem of control and quality of agricultural products is relevant for agro-industrial production. To determine the quality indicators, for example, milk, various indirect methods are used, but they are complex, some require special preliminary preparation of the sample. We need methods that will meet the following requirements: simplicity, speed and mobility. The identification of the electrophysical properties of biological objects can become the basis for the development of an electromagnetic method that will meet the above conditions. The article considers processes based on a change in the voltage (output signal) of a parallel oscillatory circuit in which an inductive cell contains the studied agricultural products. (Research purpose) The research purpose is in developing a device for determining the electrophysical properties of biological objects, analyzing the results of the study, obtaining the dependences of the output signal of the resonant amplifier on the frequency of the generator. (Materials and methods) The article presents studies of the resonant processes occurring in the simplest parallel oscillatory LC circuit. The article analyses the effect on the output parameters of a parallel oscillatory LC circuit when its inductance changes by placing various substances in an inductive coil. (Results and discussion) The article presents a block diagram of an electromagnetic device for determining and studying the electrophysical properties of biological objects. The block diagram is implemented directly into an electromagnetic device. Authors created a program in the MATLAB package for processing the experimental data. Based on the results of processing, authors got frequency dependencies for various biological objects of agriculture. (Conclusions) The processing of an array of experimental data will allow us to determine the functional, statistical and logical dependencies between the output and input values of the presented device.

Sympathetic cooling of a trapped proton mediated by an LC circuit

Efficient cooling of trapped charged particles is essential to many fundamental physics experiments1,2, to high-precision metrology3,4 and to quantum technology5,6. Until now, sympathetic cooling has required close-range Coulomb interactions7,8, but there has been a sustained desire to bring laser-cooling techniques to particles in macroscopically separated traps5,9,10, extending quantum control techniques to previously inaccessible particles such as highly charged ions, molecular ions and antimatter. Here we demonstrate sympathetic cooling of a single proton using laser-cooled Be+ ions in spatially separated Penning traps. The traps are connected by a superconducting LC circuit that enables energy exchange over a distance of 9 cm. We also demonstrate the cooling of a resonant mode of a macroscopic LC circuit with laser-cooled ions and sympathetic cooling of an individually trapped proton, reaching temperatures far below the environmental temperature. Notably, as this technique uses only image–current interactions, it can be easily applied to an experiment with antiprotons1, facilitating improved precision in matter–antimatter comparisons11 and dark matter searches12,13.

London superconductor and time-varying mesoscopic LC circuits

In this work we study the classical and quantum dynamics of a London superconductor and of a time-dependent mesoscopic or nanoscale LC circuit by assuming that the inductance and capacitance vary exponentially with time at constant rate. Surprisingly, we find that the behavior of these two systems are equivalent, both classically and quantum mechanically, and can be mapped into a standard damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the aid of the dynamical invariant method and Fock states, we solve the time-dependent Schr\"odinger equation associated with this Hamiltonian and calculate some important physical properties of these systems such as expectation values of the charge and magnetic flux, their variances and the respective uncertainty principle.

Heisenberg Operator Approach: Nano-Mechanical Oscillator (Part 2) and the Quantum LC Circuit

With the knowledge of the new design rules in Chapter 7, we use this new insight to find the eigenvectors for the nano-vibrator problem, and then we use the same approach to examine the quantum LC circuit. While the usual approach is to use Kirchhoff’s laws to analyze a simple circuit classically, we first see that Hamilton’s equations can in fact be used, giving the same classical result. But then, using the new design rules and the knowledge of the total energy in the circuit, we identify a canonical coordinate and a conjugate momentum that have nothing to do with real space and motion of a particle of mass m. At the same time, consistent with the Schrödinger picture, we continue to see that the time evolution of an observable such as position, x(t), or current, i(t), is not part of the solution. Given that Hamilton’s equations give the same result as Kirchhoff’s law but the quantum solution does not, reinforces the idea that the quantum description is showing features that cannot be imagined with a viewpoint based on classical (i.e. non-quantum) analysis.

Quantum Dynamics: Resonance and a Quantum Flip-Flop

This chapter begins the discussion of the time evolution of an active quantum system. From the earlier chapters, time dependent physics has been observed through the presence of the time evolution of the phase of each eigenstate. The Hamiltonian itself is time independent. This represents the same kind of evolution of a classical system like the vibration of a tuning fork when it has been struck or the oscillation of an LC circuit if the capacitor is charged to some voltage and then the switch is closed. In the quantum case, the Hamiltonian has also been time independent. The time evolution evolves according the full-time dependent Schrödinger equation, depending only on a single initial condition of the state vector or wave function and the corresponding time evolution of the phase factor for each eigenstate. However in this chapter, we consider the case of when there is a time dependent Hamiltonian such as a sinewave generator or laser. As in the case of resonant tunneling, we see the importance in dynamics of resonant coupling. With an oscillating potential energy term, we see the presence of Rabi oscillations in the probability amplitude of a two-state system on resonance, which can be viewed as a quantum flip-flop between two states of a quantum bit (qubit).